Hardly. Hamlet's situation is indeed awful and I would not envy it, but to compare it with losing literally everything in a matter of moments is the self-dramatization that Hamlet sometimes goes for but is ultimately ungrounded. However, The Book of Job stands as an example to us all about the nature of loss and a reminder of where we stand in the face of God.

For a deliberate parallel in a play to Job from the same time period, see Christopher Marlowe's The Jew Of Malta, which was hugely successful at the time and was an early influence to Shakespeare. His brilliant revisions on some of the ideas and characters presented therein arrive in The Merchant of Venice.

If you're asking after the probability that Shakespeare was THINKING of the Book of Job when he wrote Hamlet's lines, I think it unlikely. I don't think "Fortune" was associated with the Job story in Sh's mind, though the story of Job losing everything and then getting it back is reminiscent of the "Fortune's wheel" image quite dear to the Renaissance. The Job story, to the Elizabethan mind, probably represents more a parable of the inscrutability of God's ways and man's responsibility to trust in the divine will. Shakespeare does mention Job a couple of times (both in reference to Falstaff, as it happens); but in both instances the pertinent reference is poverty: "as poor as Job" appears to have been a common simile.

If your question more generally is whether Job's sufferings can be seen as a paradigm for the panoply of sufferings Hamlet associates with the human predicament (the "whips and scorns of Time," and so forth), I guess you could make the case. But I don't find the parallels particularly compelling.